[arxiv:physics.data-an:0808.0012]
Lectures on Probability, Entropy, and Statistical Physics by Ariel Caticha
Abstract: These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in principle be followed by an ideally rational mind when discussing scientific matters? What makes one statement more plausible than another? How much more plausible? And then, when new information is acquired how do we change our minds? Or, to put it differently, are there rules for learning? Are there rules for processing information that are objective and consistent? Are they unique? And, come to think of it, what, after all, is information? It is clear that data contains or conveys information, but what does this precisely mean? Can information be conveyed in other ways? Is information physical? Can we measure amounts of information? Do we need to? Our goal is to develop the main tools for inductive inference–probability and entropy–from a thoroughly Bayesian point of view and to illustrate their use in physics with examples borrowed from the foundations of classical statistical physics.

1 [eV] ≡ 1.6021892 · 10^-19 [Joule] ≡ 1.6021892 · 10^-12 [erg] .

The confusion is because the same units are used to denote two separate quantities which happen to have similar magnitudes for a commonly encountered spectral model, Bremsstrahlung emission.

1. the frequency ν, or wavelength λ, of a photon: As Planck discovered, the energy of a photon is directly related to the frequency ν,
   

   E = h · ν ≡ h · c / λ ,

   where h=6.6261760 · 10^-27 [erg s] is Planck’s constant and c=2.9979246 · 10¹⁰ [cm s^-1] is the speed of light in vaccum. When λ is given in [Ångström] ≡ 10^-8 [cm], we can convert it as

   [keV] = 12.398521 / [Å] ,

   which is an extraordinarily useful thing to know in high-energy astrophysics.

2. the temperature T of a gas or plasma: Here we look to thermodynamics, which relates the kinetic energy of random motion of particles in a gas to a gross property, the temperature of the gas,
   

   E = k_B · T ,

   where k_B = 1.3806620 · 10^-16 [erg K^-1] is Boltzmann’s constant. Then, a temperature in degrees Kelvin can be written in units of keV by converting it with the formula

   [keV] = 8.6173468 · 10^-8 · [K] ≡ 0.086173468 · [MK] .

It is tempting to put the two together and interpret a temperature as a photon energy. This is possible for the aforementioned Bremsstrahlung radiation, where plasma at a temperature T produces a spectrum of photons distributed as e^{-h ν / k_B T} and it is possible to tie the temperature to the photon energy at the point where the numerator and denominator have the same numerical value. For example, a 1 keV (temperature) Bremsstrahlung spectrum extends out to 1 keV (photon energy). X-ray Astronomers use this as shorthand all the time, and it confuses the hell out of everybody else.